Representations of Clifford Algebras on Function Spaces on the Cantor Set

We give a representation of the (infinite-dimensional) complex Clifford algebra on the Hilbert space of square-integrable complexvalued functions on the Cantor set.     

Measurement of macroscopic and microscopic thermal neutron cross sections of V,Co, Cu,In, Dy and Au using neutron self-absorption properties

In this study, the total thermal neutron macroscopic and microscopic cross sections of V, Co, Cu, In, Dy and Au were measured using neutron self-absorption properties. Pure foils of these elements with various thicknesses were irradiated using a 5 Ci²³⁸Pu–Be source. After the irradiation, the gamma-spectra of their radionuclides were recorded by an HpGe detector. The gamma-photopeak areas of interest were determined by evaluating the gamma-spectra obtained from the foils. They were plotted as a function of foil thickness for each element. Then a non-linear least-squares fitting method was applied to the functions, and the total thermal neutron macroscopic and microscopic cross sections of V, Co, Cu, In, Dy and Au were obtained.     

On calculation of thermal conductivity from Einstein relation in equilibrium molecular dynamics

In equilibrium molecular dynamics, Einstein relation can be used to calculate the thermal conductivity. This method is equivalent to Green-Kubo relation and it does not require a derivation of an analytical form for the heat current. However, it is not as commonly used as Green-Kubo relationship. Its wide use is hindered by the lack of a proper definition for integrated heat current (energy moment) under periodic boundary conditions. In this paper, we developed an appropriate definition for integrated heat current to calculate thermal conductivity of solids under periodic conditions. We applied this method to solid argon and silicon based systems; compared and contrasted with the Green-Kubo approach.     

Solution of magnetohydrodynamic flow in a rectangular duct by Chebyshev collocation method

In this study, matrix representation of the Chebyshev collocation method for partial differential equation has been represented and applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Numerical solution of velocity and induced magnetic field is obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. The Chebyshev collocation method is used with a reasonable number of collocations points, which gives accurate numerical solutions of the MHD flow problem. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number H≤1000. Copyright © 2010 John Wiley & Sons, Ltd.     

Cyclobutane-substituted diacetamido sulfides and 2,5-diacylthiophenes

A general and convenient route for the synthesis of 2,5-di[1-methyl-1-arylcyclobutane-3-yl]- thiophenes 4a–c and bis[1-methyl-1-arylcyclobutane-3-yl]-2-(2-oxyethtylamido)thiazole sulfides 7a–c is reported. The characterization of these compounds was obtained by elemental analyses, IR, ¹³C, and ¹H NMR techniques. © 2003 Wiley Periodicals, Inc. 15:26–31, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/.hc10207